You want force 1 to equal half of force 2. Everything in the numerators will cancel out, which is why your professor removed the gravitational constant. What is the distance force 2 acts over? What about force 1?

I thought you wanted to know how far you have to be for your weight to be half?? Whats 9.816 coming from??

Say your weight is 100 pounds or 444.8 newtons. 100 pound in kilograms is equal to 45.4. Plug that in.
444.8=G*5.974x10^24*45.4/r^2
From here all you have to do is some algerbra to get the distance(r), which is in meters.